Geophys. J. Int. (2018) 214, 282–301 Advance Access publication 2018 April 05 GJI Seismology

doi: 10.1093/gji/ggy134

Deep structure of Pyrenees range (SW Europe) imaged by joint inversion of gravity and teleseismic delay time Gr´egory Dufr´echou,1 Christel Tiberi,2 Roland Martin,1 Sylvain Bonvalot,1 S´ebastien Chevrot1 and Lucia Seoane1 1 G´ eosciences

Environnement Toulouse, Observatoire Midi-Pyr´en´ees, CNES, CNRS, IRD, UPS, 31400 Toulouse, France. E-mail: [email protected] 2 G´ eosciences Montpellier, CNRS, Univ. Montpellier, 34090 Montpellier, France

Received 2018 March 19; in original form 2017 December 22

SUMMARY We present a new model of the lithosphere and asthenosphere structure down to 300 km depth beneath the Pyrenees from the joint inversion of recent gravity and teleseismic data. Unlike previous studies, crustal correction was not applied on teleseismic data in order (i) to preserve the consistency between gravity data, which are mainly sensitive to the density structure of the crust lithosphere, and traveltime data, and (ii) to avoid the introduction of biases resulting from crustal reductions. The density model down to 100 km depth is preferentially used here to discuss the lithospheric structure of the Pyrenees, whereas the asthenospheric structure from 100 to 300 km depth is discussed from our velocity model. The absence of a high density anomaly in our model between 30 and 100 km depth (except the Labourd density anomaly) in the northern part of the Pyrenees seems to preclude eclogitization of the subducted Iberian crust at the scale of the entire Pyrenean range. Local eclogitization of the deep Pyrenean crust beneath the western part of the Axial Zone (west of Andorra) associated with the positive central density anomaly is proposed. The Pyrenean lithosphere in density and velocity models appears segmented from east to west. No clear relation between the along-strike segmentation and mapped major faults is visible in our models. The Pyrenees’ lithosphere segments are associated with different seismicity pattern in the Pyrenees suggesting a possible relation between the deep structure of the Pyrenees and its seismicity in the upper crust. The concentration of earthquakes localized just straight up the central density anomaly can reflect the subsidence and/or delamination of an eclogitized Pyrenean deep root. The velocity model in the asthenosphere is similar to previous studies. The absence of a high-velocity anomaly in the upper mantle and transition zone (i.e. 125 to 225 km depth) seems to preclude the presence of a detached oceanic lithosphere beneath the European lithosphere. Key words: Joint inversion; Seismic tomography; Gravity anomalies and Earth structure; Continental margins: convergent; Europe; Seismicity and tectonics.

1 I N T RO D U C T I O N The Pyrenees correspond to a roughly EW-trending ca. 450 km long and ca. 125 km wide continental fold-and-thrust belt in SW Europe resulting from the convergence of Eurasia and Iberia plates (Vissers & Meijer 2012a,b, and references therein; Fig. 1a). The Pyrenees’ components were affected by a complex geodynamic evolution through two major periods: (i) the Variscan cycle that encompasses the Paleotethys subduction and later collision between Laurussia and Gondwana (Matte 1986; Burg et al. 1994), and (ii) the Alpine cycle through the opening of the Bay of Biscay and the formation of the Pyrenees from the convergence of Iberia and Eurasia plates (Le Pichon et al. 1970; Sibuet et al. 2004; Vissers & Meijer

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2012a,b). Numerous geophysical and geological experiments have been conducted in the Pyrenees, where strong controversies are still prevailing concerning the global rate of shortening of the mountain range and the relative displacement of Iberia and Eurasia plates during the Cretaceous (e.g. Vissers & Meijer 2012a,b; Vanderhaeghe & Grabkowiak 2014; Barnett-Moore et al. 2016). Two kinematic scenarios generally imply: (i) a mainly sinistral strike-slip displacement occurring along the North Pyrenean Fault (e.g. Le Pichon et al. 1970; Mattauer & S´eguret 1971; Choukroune & Mattauer 1978), or (ii) a scissor-type opening implying the simultaneous subduction of a ca. 300 km wide ocean or exhumed mantle domain between Iberia and Eurasia at the Aptian (e.g. Sibuet et al. 2004; Vissers & Meijer 2012a,b). An alternative scenario also combines a complex

The Author(s) 2018. Published by Oxford University Press on behalf of The Royal Astronomical Society.

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Deep structure of Pyrenees range

Figure 1. (a) Simplified tectonic map of the Pyrenees (modified from Mouthereau et al. 2014); SPZ: South Pyrenean Zone; SPFT: South Pyrenean Frontal Thrust; AZ: Axial Zone; NPZ: North Pyrenean Zone; NPFT: North Pyrenean Frontal Thrust; NPF: North Pyrenean Fault; PF: Pamplona Fault. (b) Crustal thickness (i.e. Moho depth) modified from Chevrot et al. (2014).

evolution of strike-slip movement during the Jurassic-Early Aptian with orthogonal extension related to the opening of the Bay of Biscay (Jammes et al. 2009). Despite numerous geophysical studies performed during the last decades to image the Pyrenean lithosphere (e.g. Gallart et al. 1980, 1981; Hirn et al. 1980; Daigni`eres et al. 1981,1982; ECORS Pyrenees group 1988; Choukroune 1989; Roure et al. 1989; Torn´e et al. 1989; Choukroune et al. 1990; Nolet 1990; Daigni`eres et al. 1994; Corchete et al. 1995; Souriau & Granet 1995; Pous et al. 1997; Vacher & Souriau 2001; Gunnell et al. 2008; Souriau et al. 2008; Carballo et al. 2014; Chevrot et al. 2014; Macquet et al. 2014; Wang et al. 2016; Bonnin et al. 2017; Martin et al. 2017; see also Section 2Contract Rep.), the deep structure of the Pyrenees remains uncertain. For example, the depth of the lithosphere–asthenosphere boundary beneath the

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Pyrenees ranges from ca. 90 to 160 km depending on authors and techniques employed (Zeyen & Fernandez 1994; Pous et al. 1997; Roca et al. 2004; Gunnell et al. 2008; Campany`a et al. 2012; Carballo et al. 2014). A better knowledge of the deep structure of the Pyrenees will provide key constraints to improve our understanding of the Pyrenean geodynamics. During the PYROPE and IBERARRAY experiments, conducted respectively in France and Spain, 130 broad-band stations and two dense profiles of medium band seismic stations were deployed across the Pyrenees (2009–2013). The resulting tomographic images (Chevrot et al. 2014) exclude scenarios involving subduction of an oceanic lithosphere beneath the Pyrenees and suggest an along-strike segmentation of the lithospheric structure. Geophysical data are frequently combined in cooperative studies in order to bring more constraint to the knowledge of the lithospheric structures, especially in orogens where interactions between various processes often lead to complex lithospheric structures. In particular, gravity data are often combined with other data sets to constrain lithospheric structures. Carballo et al. (2014) used elevation, geoid height and surface heat flow with gravity anomaly to model the lithospheric structure from the Pyrenees to the Tell Atlas Mountains in Algeria. Vacher & Souriau (2001) built a 3-D lithospheric-scale density model of the Pyrenees and showed that Bouguer anomalies constrained by seismic images and petrology provide valuable information on the deep structure of an orogen. Furthermore, recent geophysical studies (Wang et al. 2016; Martin et al. 2017) have demonstrated the potential of seismic and gravity data to image crustal and lithospheric structures in the Pyrenees. In addition to the recent PYROPE and IBERARRAY experiments, during the last several decades thousands of gravity stations were acquired in the Pyrenees and surrounding basins and compiled by the International Gravimetric Bureau (BGI: http: //bgi.obs-mip.fr/; Fig. 2a). In parallel, supported by the International Gravimetric Bureau, new gravity stations were acquired to complete the gravity cover of the eastern Pyrenees in France. We propose here to combine all available gravity and recent seismic data acquired during PYROPE and IBERARRAY experiments in a joint inversion in order to reconsider the problem of imaging the deep lithosphere and upper-mantle structures of the Pyrenees. This joint inversion leads to a new density and velocity model of the deep structure of the Pyrenees that will complete and validate geological interpretations of previous regional tomography models (Souriau et al. 2008; Chevrot et al. 2014). The inversion method of ground gravity measurements and teleseismic delay times is based on the work of Zeyen & Achaueur (1997), later improved by a 3-D ray tracing and independent density and velocity model parameterization (Tiberi et al. 2003). We then compare our results with previous geophysical models and discuss them in terms of tectonic processes involved in the Pyrenees formation.

2 TECTONIC AND GEOPHYSICAL FRAMEWORK The Pyrenees orogen (Fig. 1a) is composed of (i) the North Pyrenean Zone, corresponding to the retro-wedge dominated by Mesozoic sediments containing Palaeozoic basement; (ii) the Axial Zone, mostly located in the central Pyrenees and composed of Palaeozoic rocks, intensely deformed, metamorphosed and intruded by large granitic domes during the Variscan orogeny and then deformed during Alpine orogeny. The North Pyrenean Zone and the Axial Zone are separated by the North Pyrenean Fault (NPF; Fig. 1a) along part

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Figure 2. (a) Location of the gravity stations (source: Bureau Gravim´etrique International) and seismologic stations (source: PYROPE project; Chevrot et al. 2014) used for joint inversion. (b) Map of the complete Bouguer gravity anomaly. (c) Map of the complete Bouguer gravity anomaly upwards continued to 3 km used for joint inversion.

of their contact; and (iii) the South Pyrenean Zone (SPZ; Fig. 1a), which corresponds to the pro-wedge dominated by Mesozoic and Cenozoic sediments. At the north of the Pyrenees orogen, the Aquitanian foreland basin corresponds to a large retro-foreland basin separated from the North Pyrenean Zone by the North Pyrenean Frontal Thrust (NPFT; Fig. 1a). At the south of the Pyrenees orogen, the Ebro foreland basin (Fig. 1a) is overthrust by the South Pyrenean Zone along the South Pyrenean Frontal Thrust (SPFT; Fig. 1a). The deep Pyrenean crustal structure was imaged by several seismic profiles transverse to the Pyrenean general trend including the ECORS Arzacq and ECORS Pyrenees seismic profiles in the western and central parts of the orogen and several long-range P wave reflection profiles (Hirn et al. 1980, Daigni`eres et al. 1981,1982; Gallart et al. 1981; S´eguret & Daignieres 1986; ECORS Pyrenees group 1988; Choukroune et al. 1990). These profiles have shown that the Pyrenees form an asymmetric double wedge structure displaying northward-directed thrust in France and southward-directed thrust in Spain above a north dipping slab of Iberian continental lithosphere. They have also evidenced an abrupt Moho jump, located ca. 30 km deep beneath the Aquitanian basin and going down to 50 km beneath northern Iberia (i.e. Moho step of ca. 20 km; Fig. 1b). The Pyrenean Moho’s jump decreases eastwards to reach its minimum (ca. 5 km) in the eastern Pyrenees (Gallart et al. 1980; Chevrot et al. 2014; Mancilla & Diaz 2015). Gravity modelling performed along the ECORS profiles also confirmed the asymmetrical shape of the Pyrenean crust (Torn´e et al. 1989). Ledo et al. (2000), from a 3-D electrical conductivity model of the Pyrenean lithosphere, identified a high conductivity zone in the lower crust interpreted as partial melting of the subducted Iberian lower crust. Two teleseismic P-to-S converted waves were performed along two

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dense transects across the central and western Pyrenees (Chevrot et al. 2015). They support the previous interpretation of the ECORS Arzacq profile proposed by Teixell (1998) and suggest the subduction of thinned Iberian crust down to ca. 70 km. More recently, Wang et al. (2016) presented a 3-D velocity model of the lithosphere beneath the western Pyrenees from full waveform inversion of teleseismic P waves confirming the emplacement of subcontinental mantle at shallow crustal levels beneath the Maul´eon basin. Souriau et al. (2008) used teleseismic P and PKP traveltime to provide a new tomographic model of the Pyrenean lithosphere down to 200 km. They identified a high-velocity zone in the eastern– central Pyrenees interpreted as a detached portion of the Tethys slab and suggested the presence of Variscan NW-trending low-velocity structures. However, Chevrot et al. (2014) stated that this study suffered from a poor quality of manual picks and small N–S aperture of the seismological array that limit the resolution of the deeper parts of the model. Chevrot et al. (2014) exploited the newly acquired seismic data of PYROPE and IBERARRAY experiments to obtain a new tomographic model of SW Europe from the Massif Central to central Iberia. They exclude scenarios involving subduction of oceanic lithosphere beneath the Pyrenees and suggest an along-strike segmentation of the lithosphere by transverse structure oriented NNW-SSE. The lithospheric structure of the Pyrenees and adjacent basins deduced from ambient noise tomography evidences two unusual velocity structures. The first one is located beneath the SE part of the Massif Central associated with a shallow Moho, and the second in the central Pyrenees shows the presence of Iberian crust underthrust beneath the Eurasian crust (Macquet et al. 2014).

Deep structure of Pyrenees range 3 METHODOLOGY

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the southern Massif Central is associated with low gravity anomaly ranging from ca. −60 to −30 mGal.

3.1 Data 3.1.1 Gravity data

3.1.2 Traveltime data

The Gravity cover of the study area includes 62 065 ground measurements provided by the Bureau Gravim´etrique International (Fig. 2a). In this data set, 332 new stations were acquired in the eastern part of the Pyrenees by G´eosciences Environnement Toulouse and G´eosciences Montpellier laboratories with the support of the Bureau Gravim´etrique International using a CG5 Scintrex gravimeter (1 μGal resolution, < 5 μGal repeatability). The distribution of gravity data in the study area is inhomogeneous, with a variable station spacing generally less than 1 km, except in the central part of the Pyrenees where high relief hampered data acquisition. Freeair and Bouguer corrections were calculated using the International Association of Geodesy 1967 formula. An average density of 2.67 g cm−3 is used to correct from the topographic effect. The complete Bouguer correction was performed by applying a ground correction derived from 90 m resolution digital elevation model (SRTM90) using Gravsoft software (Forsberg & Tscherning 2008) with a radius of inner and outer zones of 100 km. We performed a slight upward continuation of the data of 3 km using Geosoft Oasis Montaj in order to be above the causative sources of our density model and to be consistent with the joint parametrization (see the following section). We filtered the gravity data to limit the effect of surficial short wavelength structures, not modelled in our lithospheric imaging. We gridded the resulting complete Bouguer anomaly (Fig. 2b) and 3 km upward continued complete Bouguer anomaly (Fig. 2c) on 5 km grid maps with a minimum curvature algorithm (Briggs 1974). We finally used the resulting upward continued complete Bouguer anomaly grid (62 065 points, Fig. 2c) in the joint inversion. As portrayed by Casas et al. (1997), the Pyrenees are associated with a large negative anomaly (i.e. from ca. −120 to −90 mGal; Figs 2b and c) mainly located in Spain and caused by the thick Pyrenean crustal roots (Fig. 1b). The eastern termination of this negative anomaly occurs at the east of Andorra and corresponds to the eastward thinning of the Pyrenean crust (Fig. 1b). A slight northeastward continuation of this negative anomaly occurs in France (NW of Andorra; Fig. 2b) and corresponds to a local thicker continental crust (Fig. 1b). The western termination of the Pyrenean negative anomaly broadly corresponds to the westward disappearance of outcrops of Palaeozoic units in the Axial Zone. Note that the deepest Moho located in the western part of the Pyrenees determined from receiver function (Chevrot et al. 2014; Mancilla & Diaz 2015) is not encompassed within the main negative anomaly caused by crustal thickening (Figs 1b and 2b and c). The Aquitanian and Ebro basins are roughly associated with a higher gravity response than surrounding domains, respectively ranging from ca. −20 to 5 mGal and ca. −35 to −20 mGal, materializing the sedimentary filling within the basins. The North Pyrenean Zone and the South Pyrenean Zone are dominated by a gravity response of ca. −50 mGal. The Labourd and Saint-Gaudens positive gravity anomalies clearly visible on the Bouguer gravity map (Fig. 2a) were explained by the emplacement of high density body at upper crustal level (Grandjean 1994; Corpel & Casas 1996; Pedreira et al. 2007). The Labourd gravity anomaly is also interpreted by the emplacement of mantle material within the crust (Wang et al. 2016). These crustal anomalies were previously imaged by gravity data (Grandjean 1994), seismic crustal tomography (Souriau & Granet 1995; Souriau et al. 2008) and ambient noise surface waves (Villase˜nor et al. 2007). In the NE of the study area,

The teleseismic P traveltime residuals used in this study were previously compiled and used in Chevrot et al. (2014). They come from the temporary PYROPE (http://dx.doi.org/10.15778/RESIF.X720 10) and IBERARRAY experiments (https://doi.org/10.7914/SN/IB) (broad-band stations, Fig. 2a). Data from the permanent broadband stations of the R´eseau Large Bande Permanent (RLBP; http://rlbp.unistra.f r), the short-period stations of the R´eseau National de Surveillance Sismique (R´eNaSS; http://renass.unistra.f r) on the French side, the permanent broad-band stations of the Instituto Geogr´afico Nacional (IGN; http://www.ign.es) and of the Institut Cartogr`afic i Ge`ologic de Catalunya (ICGC; http://www.icgc.cat) in the Pyrenees and surrounding domain were also added (Chevrot et al. 2014). We used P wave traveltimes from 162 teleseismic events with a moment magnitude larger than 5.8 and recorded between January 2008 and September 2013 in the epicentral distance range 30◦ –90◦ (Fig. 3). The traveltime residuals are calculated by subtracting the theoretical traveltime computed in the ak135 reference earth model as described in Chevrot et al. (2014). For each event, the mean residual was then removed to obtain relative time residuals and get rid of common errors resulting from source mislocation and uncertainty on the origin time. The obtained data set is composed of 2851 relative traveltime residuals over the whole network (166 stations).

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3.2 Joint inversion of gravity and delay times 3.2.1 Joint inversion scheme The joint inversion method used in this study was introduced by Zeyen & Achauer (1997) and then further modified by Tiberi et al. (2003). It has been successfully applied in various geodynamical settings (Tiberi et al. 2003; Tiberi et al. 2008; Basuyau & Tiberi 2011; Basuyau et al. 2013). This method is based on the coherent behaviour and the approximate linear relationship between P-wave velocity and density perturbations (Birch 1961; Abers 1994): V p = B.ρ, where B is a coefficient depending on rock type and mostly ranges from 2.5 to 3.5 km s−1 g−1 cm3 (Birch 1961). Three unknown parameters are considered in the inversion process: (i) the P-wave velocity anomaly (Vp/Vp); (ii) the density contrast (ρ); (iii) the B coefficient. The joint inversion is based on a Bayesian approach requiring a priori 3-D velocity and density models in order to reduce the set of possible solutions. The method starts with those a priori models (see the next section) and iteratively modifies them to jointly minimize the Bouguer gravity anomaly and traveltime residuals in a least-squares sense. We performed an optimization algorithm that invokes three steps for each iteration: (1) The gravity forward calculation is performed at iteration n by applying Blakely (1995) forward method on the density contrasts obtained at iteration n − 1. We compute the delay times at iteration n using the bending method of Steck & Prothero (1991). The seismic rays are propagated in the 3-D velocity model obtained at iteration n − 1. The B coefficient is computed based on the correlation between density and velocity n − 1 models.

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Figure 3. Azimuthal distribution of the first P-wave teleseismic events used for this study (M > 5.8, AZ = [25–100]). The projection is centred on the Pyrenees.

(2) The delay times and gravity anomaly for iteration n are then compared to the observed data, and new residuals are computed. (3) The new residuals are finally inverted in the least-squares sense to obtain a new density and velocity perturbation distribution. These new density and velocity models become the starting models for iteration n + 1. This inversion scheme is iterated until it reaches a pre-defined number of iterations or when the observed and calculated data difference falls below a given threshold. We estimate the success of the inversion through the root mean square (rms) reduction, final standard deviation of parameters and recovered data, and synthetic tests. Readers can refer to Tiberi et al. (2003, 2008) for further details on the joint inversion scheme.

3.2.2 Model parameterization The inversion requires one model for density and one for velocity. They are both discretized into N layers. Each layer is subdivided into rectangular blocks to which a density contrast is assigned (Blakely 1995). Each density block contains a velocity node to fulfil the formalism of Steck & Prothero (1991) and to warrant a good estimation of B value in each layer. Between those nodes, the velocity is interpolated with a gradient method (Thurber 1983). The density block dimension and the velocity node spacing are dictated by wavelength content of the gravity anomaly and by the seismic station coverage. It should also optimize the ratio between the number of model parameters and observed data. As the inversion problem

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is already ill-posed, we do not try to increase its inherent underestimation by having unconstrained density blocks and velocity nodes (e.g. Menke 1984). We tested different nodes/blocks configuration, and horizontal and vertical extensions of the initial model to evaluate their influence on the final solution. We finally opted here for a regular 26 × 23 blocks/nodes parametrization. This regular gridding allows for a homogeneous a priori distribution of sources and for a better coherency between density and velocity anomalies’ shape and size. The block dimension and node spacing are 25 km in east–west and north–south directions, except for the outermost edges, where larger blocks and node interval (100 km) were chosen to absorb the boundary effect. We divided our models into seven layers (Table 1). The first layer starts from 3 km of elevation down to 30 km depth to take into account the topography. The 3-D ray tracing starts from the seismic station elevation, so that even if not fully resolved because of poor ray crossing (Zeyen & Achauer 1997), the velocity and density first layer contain consistent information and include topography. A priori information is used during inversion to constrain the models, limit the effect of noise and reduce the impact of an ill-posed problem. First, initial standard deviations are assigned to both data and parameters. We set the standard deviations for gravity and delay times data to the estimated accuracy of gravity measurement and traveltime picks (ca. 2 mGal and 0.01 s). From our tests, we decide to favour a homogeneous a priori constraint by settling constant standard deviations for density (0.01 g cm−1 ) and velocity (0.01 km s−1 ). For density and velocity models, the a priori model values are based on the ak135 reference Earth model (Kennett et al. 1995) and

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Table 1. Parametrization of density and velocity initial models for the joint inversion. The velocity nodes are located at the centre of each density block. The correlation coefficient corresponds to the level of coherence between velocity and density at the end of the inversion. Layer interfaces depth (km) −3∗

to 30 30–60 60–100 100–150 150–200 200–250 250–300

∗ The

Velocity initial (km s−1 )

Density initial (g cm−1 )

Final B value

Correlation coefficient

6.15 8.03 8.04 8.05 8.2 8.4 8.5

2.67 3.00 3.30 3.33 3.35 3.39 3.50

3.726 0.684 2.828 3.223 3.354 3.420 3.527

0.575 0.107 0.417 0.726 0.900 0.948 0.956

uppermost interface of the first layer is 3 km in elevation in order to include the topographic effect.

adapted to our own layering (Table 1). Initial value of B was set to 3 for all layers. The maximum number of iterations was fixed to five. We add a smoothing constraint to avoid sharp and strong oscillations between neighbouring density blocks or velocity nodes (Zeyen & Achauer 1997). In order to choose the optimum smoothing parameters, we followed the L-curve method (see Hansen 2001; Foulger et al. 2013). We used the trade-off curves from a selection of models to investigate the balance between model roughness (quantified by the difference between the extreme positive and negative wave speed/density contrasts) and root mean square prediction error reduction (in per cent). We also tested initial standard deviation parameters. After all these tests, the smoothing density and velocity constraints are respectively set to 0.003 and 0.001.

3.2.3 Model resolution We estimate the resolution of our final model from different factors. First, the calculation of resolution matrix diagonal terms is performed at the end of the inversion process. The resolution matrix relates true and estimated models and should thus be close to identity to provide unbiased results (Menke 1984). Values of the diagonal terms are strongly dependent on the smoothing constraint (the smoother, the smaller terms). As expected, the resolution of inverted density parameters (Fig. 4) is larger in crustal layers (i.e. up to 60 km depth) with a maximum diagonal term of ca. 1.0 for the first layer. It then strongly decreases with depth (locally up to ca. 0.8 in the 30–60 km layer). The average resolution diagonal term for velocity parameters is ca. 0.3, with values up to 0.6 locally (Fig. 5). The best resolution is unsurprisingly obtained in the central part of the study area, beneath the Axial Zone and the North Pyrenean Zone (see Fig. 1a) where ray crossing and coverage are the highest. The best resolved depth interval is between 100 and 200 km (Fig. 5), similar to Chevrot et al. (2014). Second, to evaluate the linear resolving power of the inversion, we test the ability of our data sets to retrieve a checkerboard model in the lithosphere and asthenosphere. This classic approach allows to (i) define areas that are well constrained, (ii) estimate the vertical smearing along the subvertical teleseismic rays, and (iii) assess the shortest anomaly wavelength that can be retrieved from our ray coverage. The number and size of layers, the velocity nodes and the gravity blocks are similar to the initial model presented in Table 1. We alternate positive and negative perturbations in layers 2 (30–60 km, i.e. lithosphere/subcrustal perturbations) and 5 (150–200 km, i.e. asthenosphere perturbations). The perturbations of the checkerboard pattern size are [3 × 3] density blocks and velocity nodes, and their amplitude is ±5 per cent relative to the a priori density and velocity model (Figs 6 and 7). These synthetic structures with identical model parameterization were jointly inverted using the real data distribution. The resulting density and velocity models are presented in Figs 6 and 7. Narrower

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synthetic anomalies within a [2 × 2] density blocks and velocity nodes checkerboard pattern were also tested. Density and velocity blocks were correctly recovered in the layer 30–60 km, but velocity nodes were inadequately resolved deeper, even in the middle of the model where the best resolution is expected. Finally, we also estimate the smearing effect and lateral resolution with a spike test of three smaller perturbations sizing [2 × 2] density blocks and velocity nodes with an amplitude of ±5 per cent relative to the a priori density and velocity model in the layer 30–60 km (Figs 8 and 9). The size and shape of the recovered velocity checkerboard confirm the ability of the inversion process to retrieve perturbations at lithospheric and asthenospheric level, as well as its capacity to resolve lateral contrasts (Figs 7 and 9). As expected in such teleseismic tomography, vertical smearing is present and affects the layers above and below the input anomalies (Foulger et al. 2013). The amplitude of the initial velocity perturbation is thus distributed in three layers, and is consequently reduced in the original one (at 30–60 or 150– 200 km). The checkerboard size and shape of the density anomaly is well retrieved in layer 30–60 km (Fig. 6), highlighting the good lateral resolution of the density for crustal/lithospheric depth (30 to 60 km) consistent with the model resolution (Fig. 4). Similarly to the velocity model, but to a lesser extent, the checkerboard pattern in layer 30–60 km is smeared down to 100 km depth. The geometry of the checkerboard pattern at 150 km is weakly distinguishable, limited by the poor vertical resolution of the density model. The decrease in resolution observed in the Ebro basin (Spanish part) can be explained by the lack of southeast teleseismic events, which prevent us from retrieving more complete information on the structures in that region (Fig. 3). Finally, the good convergence of the inversion is estimated from the decrease of the rms through five iterations. The gravity residuals decrease from 22.57 to 2.03 mGal (90.99 per cent) and the delay time residuals decrease from 0.37 to 0.2 s (47.88 per cent; Fig. 10). These results are broadly comparable to the rms decrease obtained in previous studies in the Pyrenees, Central Mongolia and Southern Siberia for gravity data (94 per cent, Tiberi et al. 2008) and delay times (43 per cent, Tiberi et al. 2008; ca. 70 per cent Chevrot et al. 2014) attesting the stability and robustness of the inversion. The final density and velocity variations in our models range, respectively, between –0.2 and + 0.2 g cm−3 and –3 and + 3 per cent indicating reasonable values for lithospheric scale. The complete Bouguer anomaly calculated from our density model is broadly consistent with the observed complete Bouguer anomalies attesting for the accuracy of our density model (Figs 11a and b). The highest discrepancies happen for the central part of the Pyrenees, where our inversion slightly overestimates the gravity signal (Fig. 11c). The coherence between velocity and density contrast can be estimated through the B value evolution. As the joint inversion scheme

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Figure 4. Lateral resolution in the density model.

is highly non-linear, we have to restrict the variation of this parameter in a reasonable range (i.e.